Next, we assess goodness-of-fit by inspecting standardized residuals and carrying out posterior predictive checks [1]}. We generate posterior predictive samples corresponding to each training point. To validate the assumption of normality of the measurement error, we look at a Q-Q plot of standardized residuals, defined to be the difference of the observed and predicted responses and then standardized. We also compare the marginal density of the observed response variable with the marginal densities of 3 randomly chosen MCMC samples of predicted responses. We provide both the Q-Q plot of the obtained standardized residuals and the comparison of marginal density plots in Figure REF . Figure REF (a) indicates that the normality assumption is justified; furthermore, the densities of the randomly chosen predicted response samples in Figure REF (b) very closely resemble the marginal density of the observed response. Lastly, the coverage of \(95\%\)  posterior predictive intervals of the responses, averaged over all observed responses, is \(96 \%\) .
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